Distinguished Dissertations in Computer Science. Cambridge University Press, 1994. ISBN 0 521 47103 6 hardback. Publication dates 29 September 1994 (UK) and 27 January 1995 (USA).
A PDF version is available online since August 14, 2007, as permitted by Cambridge University Press, who own the copyright.
The first half develops the operational theory of a semantic metalanguage used in the second half. The metalanguage M is a simply-typed lambda-calculus with product, sum, function, lifted and recursive types. We study two definitions of operational equivalence: Morris-style contextual equivalence, and a typed form of Abramsky's applicative bisimulation. We prove operational extensionality for M---that these two definitions give rise to the same operational equivalence. We prove equational laws that are analogous to the axiomatic domain theory of LCF and derive a co-induction principle.
The second half defines a small functional language, H, and shows how the semantics of H can be extended to accommodate I/O. H is essentially a fragment of Haskell. We give both operational and denotational semantics for H. The denotational semantics uses M in a case study of Moggi's proposal to use monads to parameterise semantic descriptions. We define operational and denotational equivalences on H and show that denotational implies operational equivalence. We develop a theory of H based on equational laws and a co-induction principle.
We study simplified forms of four widely-implemented I/O mechanisms: side-effecting, Landin-stream, synchronised-stream and continuation-passing I/O. We give reasons why side-effecting I/O is unsuitable for lazy languages. We extend the semantics of H to include the other three mechanisms and prove that the three are equivalent to each other in expressive power.
We investigate monadic I/O, a high-level model for functional I/O based on Wadler's suggestion that monads can express interaction with state in a functional language. We describe a simple monadic programming model, and give its semantics as a particular form of state transformer. Using the semantics we verify a simple programming example.